Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter

The traditional empirical Bayes (EB) model is considered with the parameter being a location parameter, in the situation when the Bayes estimator has a finite degree of smoothness and, possibly, jump discontinuities at several points. A nonlinear wavelet EB estimator based on wavelets with bounded supports is constructed, and it is shown that a finite number of jump discontinuities in the Bayes estimator do not affect the rate of convergence of the prior risk of the EB estimator to zero. It is also demonstrated that the estimator adjusts to the degree of smoothness of the Bayes estimator, locally, so that outside the neighborhoods of the points of discontinuities, the posterior risk has a high rate of convergence to zero. Hence, the technique suggested in the paper provides estimators which are significantly superior in several respects to those constructed earlier.     

Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors

We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.     

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.     

前方小切口入路治疗股骨颈骨折的围术期指标观察

目的研究前方小切口入路治疗股骨颈骨折的围术期指标观察。方法选取湖北省孝感市中心医院2011年2月—2013年7月收治的98例股骨颈骨折患者,抽签随机分为对照组和观察组各49例。对照组患者采用传统后外侧入路切开复位术,观察组采用前外侧小切口入路复位术,观察两组围术期相关指标。结果观察组手术切口(7.8±1.1)cm较对照组(15.3±1.7)cm明显较小,术中出血量(107.2±21.4)m L较对照组(187.4±32.1)m L明显较低,具有统计学意义(P0.05);观察组骨折愈合率100%较对照组89.80%明显较高,观察组并发症率4.08%较对照组16.33%显著较低,具有统计学意义(P0.05)。结论前方小切口入路术切口小,术中出血量低且术后并发症较少,有利于股骨颈骨折患者病情恢复。     

2×2列联表中二属性相关的Bayes检验

2×2列联表中二属性相关的假设检验是定性数据分析中的热点问题,针对此问题的研究频率学派已做过大量的工作,其理论方法已趋于成熟.利用Bayes检验研究2×2列联表中二属性的相关性迄今为止国内外的相关文献还为数不多.将依据Bayes理论对此问题提出新的检验方法,推出其Bayes因子计算公式,利用正态近似研究三项假设计算出有关的后验概率,不仅解决了频率学派难以处理的问题,并且为吸烟有害健康提供了理论支撑.     

Existence of Bayesian Estimates for the Polychotomous Quantal Response Models

This paper investigates the existence of Bayesian estimates for polychotomous quantal response models using a uniform improper prior distribution on the regression parameters. Necessary and sufficient conditions for the propriety of the posterior distribution with a general link function are established. In addition, the sufficient conditions for the existence of the posterior moments and the posterior moment generating function are obtained. It is also found that the propriety guarantees the existence of the maximum likelihood estimate.     

基于后验概率度量的粒子滤波跟踪算法研究

 针对遮挡、光照变化、尺度变化等复杂环境中的视觉跟踪问题,提出一种基于后验概率度量的粒子滤波跟踪算法。由于后验概率指标与Bhattacharyya系数指标相比具有更强的峰值特性,采用后验概率指标作为相似性度量函数,通过粒子的更新、推广、观测、估计等步骤实现跟踪算法。通过对实际视频图像序列进行目标跟踪实验,实验结果表明:传统算法只有约50%的图像能够实现尺度自适应,而本文算法采用传统算法25%的粒子就能够收敛逼近目标的真实轨迹,达到更强的抗遮挡能力,90%以上的图像序列都能够实现良好的尺度自适应效果。     

Bayesian inference using record values from Rayleigh model with application

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.     

On the normality a posteriori for exponential distributions,using the Bayesian estimation

Summary The Bayesian estimation problem for the parameter θ of an exponential probability distribution is considered, when it is assumed that θ has a natural conjugate prior density and a loss-function depending on the squared error is used. It is shown that, with probability one, the posterior density of the Bayesian—centered and scaled parameter converges pointwise to the normal probability density. The weak convergence of the posterior distributions to the normal distribution follows directly. Both correct and incorrect models are studied and the asymptotic normality is stated respectively.